Objection 1. It would seem that Christ should not have been tempted in the desert. Because Christ wished to be tempted in order to give us an example, as stated above (Article 1). But an example should be set openly before those who are to follow it. Therefore He should not have been tempted in the desert.
Objection 2. Further, Chrysostom says (Hom. xii in Matth.): "Then most especially does the devil assail by tempting us, when he sees us alone. Thus did he tempt the woman in the beginning when he found her apart from her husband." Hence it seems that, by going into the desert to be tempted, He exposed Himself to temptation. Since, therefore, His temptation is an example to us, it seems that others too should take such steps as will lead them into temptation. And yet this seems a dangerous thing to do, since rather should we avoid the occasion of being tempted.
Objection 3. Further, Matthew 4:5, Christ's second temptation is set down, in which "the devil took" Christ up "into the Holy City, and set Him upon the pinnacle of the Temple": which is certainly not in the desert. Therefore He was not tempted in the desert only.
On the contrary, It is written (Mark 1:13) that Jesus "was in the desert forty days and forty nights, and was tempted by Satan."
I answer that, As stated above (1, ad 2), Christ of His own free-will exposed Himself to be tempted by the devil, just as by His own free-will He submitted to be killed by His members; else the devil would not have dared to approach Him. Now the devil prefers to assail a man who is alone, for, as it is written (Ecclesiastes 4:12), "if a man prevail against one, two shall withstand him." And so it was that Christ went out into the desert, as to a field of battle, to be tempted there by the devil. Hence Ambrose says on Luke 4:1, that "Christ was led into the desert for the purpose of provoking the devil. For had he," i.e. the devil, "not fought, He," i.e. Christ, "would not have conquered." He adds other reasons, saying that "Christ in doing this set forth the mystery of Adam's delivery from exile," who had been expelled from paradise into the desert, and "set an example to us, by showing that the devil envies those who strive for better things."
Reply to Objection 1. Christ is set as an example to all through faith, according to Hebrews 12:2: "Looking on Jesus, the author and finisher of faith." Now faith, as it is written (Romans 10:17), "cometh by hearing," but not by seeing: nay, it is even said (John 20:29): "Blessed are they that have not seen and have believed." And therefore, in order that Christ's temptation might be an example to us, it behooved that men should not see it, and it was enough that they should hear it related.
Reply to Objection 2. The occasions of temptation are twofold. one is on the part of man--for instance, when a man causes himself to be near to sin by not avoiding the occasion of sinning. And such occasions of temptation should be avoided, as it is written of Lot (Genesis 19:17): "Neither stay thou in all the country about" Sodom.
Another occasion of temptation is on the part of the devil, who always "envies those who strive for better things," as Ambrose says (In Luc. iv, 1). And such occasions of temptation are not to be avoided. Hence Chrysostom says (Hom. v in Matth. [From the supposititious Opus Imperfectum): "Not only Christ was led into the desert by the Spirit, but all God's children that have the Holy Ghost. For it is not enough for them to sit idle; the Holy Ghost urges them to endeavor to do something great: which is for them to be in the desert from the devil's standpoint, for no unrighteousness, in which the devil delights, is there. Again, every good work, compared to the flesh and the world, is the desert; because it is not according to the will of the flesh and of the world." Now, there is no danger in giving the devil such an occasion of temptation; since the help of the Holy Ghost, who is the Author of the perfect deed, is more powerful* than the assault of the envious devil. [All the codices read 'majus.' One of the earliest printed editions has 'magis,' which has much to commend it, since St. Thomas is commenting the text quoted from St. Chrysostom. The translation would run thus: 'since rather is it (the temptation) a help from the Holy Ghost, who,' etc.].
Reply to Objection 3. Some say that all the temptations took place in the desert. Of these some say that Christ was led into the Holy City, not really, but in an imaginary vision; while others say that the Holy City itself, i.e. Jerusalem, is called "a desert," because it was deserted by God. But there is no need for this explanation. For Mark says that He was tempted in the desert by the devil, but not that He was tempted in the desert only.
Source: Summa Theologica (New Advent)